Project 4¶
Goal 1: Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.¶
In [2]:
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import cv2
import numpy as np
import glob
import matplotlib.gridspec as gs
%matplotlib inline
I have 20 images for the camera. We have done this exercise with 1 image, but I guess with 20 images it is the same but it will improve the calibration quality.
In [3]:
# Load image
n = 2
sample_img = mpimg.imread('camera_cal/calibration{}.jpg'.format(n))
# Convert to gray
gray = cv2.cvtColor(sample_img, cv2.COLOR_RGB2GRAY)
# Find corners
nx = 9
ny = 6
ret, corners = cv2.findChessboardCorners(gray, (nx,ny), None)
if ret:
# Draw corners
cv2.drawChessboardCorners(sample_img, (nx, ny), corners, ret)
# show image
plt.imshow(sample_img)
For some images, the algorithm is not finding the corners. That seems to happen with zoomed in pictures where not all corners available, and it seems logic it will not find, as not all corners are available.
I can check if the corners have been found or not for a particular image by checking if ret is True
In [4]:
## use the corners to calibrate the camera
def calibrate_camera():
# prepare object points, like (0,0,0), (1,0,0)...(6,5,0)
# further study these two lines
objp = np.zeros((nx*ny,3), np.float32)
objp[:, :2] = np.mgrid[:nx, :ny].T.reshape(-1,2)
# Arrays to store object points and image points
objpoints = []
imgpoints = []
# List of calibration images using glob
images = glob.glob('camera_cal/calibration*.jpg')
for idx, fname in enumerate(images):
# load image and convert to single channel
img = mpimg.imread(fname)
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
# find chessboard corners
ret, corners= cv2.findChessboardCorners(gray, (nx, ny), None)
# if found, add object points and image points
if ret:
objpoints.append(objp)
imgpoints.append(corners)
# calibrate the camera
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
return ret, mtx, dist, rvecs, tvecs
In [5]:
ret, mtx, dist, rvecs, tvecs = calibrate_camera()
In [6]:
def compare_images(img1, img2, cmap=None):
# set figure layout
f, (ax1, ax2) = plt.subplots(1,2,figsize=(24,9))
f.tight_layout()
# show original image
ax1.imshow(img1, cmap=cmap)
ax1.set_title("Original Image", fontsize=50)
# show transformed image
ax2.imshow(img2, cmap=cmap)
ax2.set_title("Transformed Image", fontsize=50)
# adjust margins
plt.subplots_adjust(left=0, right=1, top=.9, bottom=0)
Goal 2: Apply a distortion correction to raw images.¶
To begin, I need to separate a few samples images. I will verify the distortion both in a chessboard image and in a test image for the project
In [7]:
# test on sample image
undist = cv2.undistort(sample_img, mtx, dist, None, mtx)
compare_images(sample_img, undist)
In [8]:
test_img = mpimg.imread('test_images/test1.jpg')
undist_img = cv2.undistort(test_img, mtx, dist, None, mtx)
compare_images(test_img, undist_img)
The differences are subtle to the naked eye, but upon closer inspection you can see the undistortion effect, specially on the lane lines
Goal 3: Use color transforms, gradients and other techniques to create a thresholded binary image¶
I will start with the simplest technique, selecting a region of interest
In [295]:
def region_of_interest(img, vertices):
"""
Applies an image mask.
Only keeps the region of the image defined by the polygon
formed from `vertices`. The rest of the image is set to black.
"""
#defining a blank mask to start with
mask = np.zeros_like(img)
#defining a 3 channel or 1 channel color to fill the mask with depending on the input image
if len(img.shape) > 2:
channel_count = img.shape[2] # i.e. 3 or 4 depending on your image
ignore_mask_color = (255,) * channel_count
else:
ignore_mask_color = 255
#filling pixels inside the polygon defined by "vertices" with the fill color
cv2.fillPoly(mask, vertices, ignore_mask_color)
#returning the image only where mask pixels are nonzero
masked_image = cv2.bitwise_and(img, mask)
return masked_image
def select_region(image):
""" 'Crop' the image to a 4-vertices polygonal image where the lane will most likely be situated """
# define shape
h, w = image.shape[:2]
vertices = np.array([[(50, h),
(int(w/2)-100, 415),
(int(w/2)+100, 415),
(w-50,h)]],
dtype=np.int32)
# apply mask
image = region_of_interest(image, vertices)
return image
Moving to color threshold
In [276]:
def color_thresh(img, thresh=(90,255)):
# isolate s channel from HLS
s_img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)[:, :, 2]
# apply color threshold
hls_binary = np.zeros_like(s_img)
hls_binary[(s_img >= thresh[0]) & (s_img <= thresh[1])] = 1
return hls_binary
Apply gradient threshold, with both gradient magnitude (combined or by axis) and direction thresholds
In [277]:
def abs_sobel_thresh(img, orient='x', sobel_kernel=3, thresh=(0,255)):
# calculate directional gradient
if orient=='x':
sobel = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
else:
sobel = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
# get absolute value
abs_sobel = np.absolute(sobel)
# scale it
scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
# create binary mask and apply threshold
grad_binary = np.zeros_like(scaled_sobel)
grad_binary[(scaled_sobel>=thresh[0]) & (scaled_sobel<=thresh[1])] = 1
return grad_binary
def mag_thresh(img, sobel_kernel=3, thresh=(0,255)):
# calculate gradient magnitude
sobelx = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobely = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
grad_mag = np.sqrt(sobelx**2 + sobely**2)
# scale it
scaled_sobel = np.uint8(255*grad_mag/np.max(grad_mag))
# create binary mask and apply threshold
grad_binary = np.zeros_like(scaled_sobel)
grad_binary[(scaled_sobel>=thresh[0]) & (scaled_sobel<=thresh[1])] = 1
return grad_binary
def dir_thresh(img, sobel_kernel=3, thresh=(0,np.pi/2)):
# calculate sobel
sobelx = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobely = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
# calculate gradient direction
grad_dir = np.arctan2(np.absolute(sobely), np.absolute(sobelx))
# create binary mask and apply threshold
grad_binary = np.zeros_like(grad_dir)
grad_binary[(grad_dir>=thresh[0]) & (grad_dir<=thresh[1])] = 1
return grad_binary
Let's visualize the effect of each transform and try to find an optimal point
In [348]:
cropped_img = select_region(cv2.cvtColor(undist_img, cv2.COLOR_RGB2GRAY))
compare_images(undist_img, cropped_img, cmap='gray')
In [367]:
color_binary = color_thresh(undist_img, thresh=(120,255))
compare_images(undist_img, color_binary, cmap='gray')
In [365]:
# gray = cv2.cvtColor(undist_img, cv2.COLOR_RGB2HLS)[:, :, 2]
gray = cv2.cvtColor(undist_img, cv2.COLOR_RGB2GRAY)
In [366]:
gradx_binary = abs_sobel_thresh(gray, orient='x', sobel_kernel=5, thresh=(20,100))
compare_images(undist_img, gradx_binary, cmap='gray')
In [368]:
grady_binary = abs_sobel_thresh(gray, orient='y', sobel_kernel=7, thresh=(30,100))
compare_images(undist_img, grady_binary, cmap='gray')
In [369]:
mag_binary = mag_thresh(gray, sobel_kernel=15, thresh=(40,120))
compare_images(undist_img, mag_binary, cmap='gray')
In [370]:
dir_binary = dir_thresh(gray, sobel_kernel=15, thresh=(0.70,1.3))
compare_images(undist_img, dir_binary, cmap='gray')
In [371]:
combined = np.zeros_like(gray)
combined[((gradx_binary == 1) | (grady_binary == 1) | (mag_binary == 1) | (color_binary==1)) & (cropped_img!=0) ] = 1
compare_images(undist_img, combined, cmap='gray')
Goal 4: Apply a perspective tranform to rectify binary image ("birds-eye view")¶
I will first test it on the undistorted chessboard image sample, before moving to the lane lines image
In [324]:
# Convert to gray and find corners
n = 3
sample_img = mpimg.imread('camera_cal/calibration{}.jpg'.format(n))
undist_sample_img = cv2.undistort(sample_img, mtx, dist, None, mtx)
gray = cv2.cvtColor(undist_sample_img, cv2.COLOR_RGB2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (nx,ny), None)
In [325]:
# define src to be the most distant corners forming a rectange
# src = corners[[0,nx,len(corners)-1-nx,len(corners)-1], 0]
src = corners[[0,nx-1,-1,-nx], 0]
src
Out[325]:
In [326]:
# create dst
offset = 100
h,w = gray.shape
dst = np.array([[offset,offset],[w-offset,offset],
[w-offset, h-offset],[offset, h-offset]],
dtype=np.float32)
dst
Out[326]:
In [327]:
M = cv2.getPerspectiveTransform(src,dst)
warped_img = cv2.warpPerspective(undist_sample_img, M, gray.shape[::-1],
flags=cv2.INTER_LINEAR)
compare_images(undist_sample_img, warped_img)
Next I will try perspective transform on a lane road. For now I will manually detect 4 points in the road, as indicated in the lessons, and figure it out later how do it in video stream automatically.
In [328]:
straight_img = mpimg.imread('test_images/straight_lines1.jpg')
plt.imshow(straight_img)
Out[328]:
In [398]:
#undistort image
undist_img = cv2.undistort(straight_img, mtx, dist, None, mtx)
# set source
#src = np.array([[611, 440],[667, 440],[1044,675],[260,675]], dtype=np.float32)
# src = np.array([[594, 450],[686, 450],[1085,700],[220,700]], dtype=np.float32)
src = np.array([[610, 440],[667, 440],[1050,675],[260,675]], dtype=np.float32)
# set destination
offset = 300
h,w = undist_img.shape[:2]
dst = np.array([[offset,0],[w-offset,0],
[w-offset, h],[offset, h]],
dtype=np.float32)
# warp image
M = cv2.getPerspectiveTransform(src,dst)
warped_img = cv2.warpPerspective(undist_img, M, (w,h),
flags=cv2.INTER_LINEAR)
draw_undist_img = np.copy(undist_img)
draw_warped_img = np.copy(warped_img)
cv2.polylines(draw_undist_img,np.int_([src]),True,color=(255,0,0), thickness=2)
cv2.polylines(draw_warped_img,np.int_([dst]),True,color=(255,0,0), thickness=3)
# plot
#plt.figure(figsize=(18,9))
#plt.imshow(draw_undist_img)
compare_images(draw_undist_img, draw_warped_img)
Out[398]:
In [400]:
compare_images(draw_undist_img, draw_warped_img)
In [397]:
plt.imshow(draw_undist_img)
Out[397]:
In [372]:
# testing it in a curved image
curved_img = mpimg.imread('test_images/test2.jpg')
undist_img = cv2.undistort(curved_img, mtx, dist, None, mtx)
# warp image
M = cv2.getPerspectiveTransform(src,dst)
warped_img = cv2.warpPerspective(undist_img, M, (w,h),
flags=cv2.INTER_LINEAR)
# plot
compare_images(undist_img, warped_img)
Goal 5: Detect lane pixels and fit to find the lane boundary.¶
In [373]:
def preprocess(img):
gray = cv2.cvtColor(undist_img, cv2.COLOR_RGB2GRAY)
#gradient
cropped_img = select_region(gray)
color_binary = color_thresh(undist_img, thresh=(120,255))
gradx_binary = abs_sobel_thresh(gray, orient='x', sobel_kernel=5, thresh=(20,100))
grady_binary = abs_sobel_thresh(gray, orient='y', sobel_kernel=7, thresh=(30,100))
mag_binary = mag_thresh(gray, sobel_kernel=15, thresh=(40,120))
dir_binary = dir_thresh(gray, sobel_kernel=15, thresh=(0.70,1.3))
combined = np.zeros_like(gray)
combined[((gradx_binary == 1) | (grady_binary == 1) | (mag_binary == 1) | (color_binary==1)) & (cropped_img!=0) ] = 1
return combined
combined = preprocess(undist_img)
combined = cv2.warpPerspective(combined, M, (w,h), flags=cv2.INTER_LINEAR)
In [385]:
plt.imshow(combined, cmap='gray')
Out[385]:
The overall idea is to split the image into thin slices, and verify the center of each lane by using the histogram peak for each slice. Let's first visualize this strategy to have an idea how it will work
I will try the same process, using Udacity's code for estimating the sliding windows
In [382]:
# Take a histogram of the bottom half of the image
histogram = np.sum(combined[combined.shape[0]/2:,:], axis=0)
# Create an output image to draw on and visualize the result
out_img = np.dstack((combined, combined, combined))*255
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0]/2)
#leftx_base = np.argmax(histogram[:midpoint])
#rightx_base = np.argmax(histogram[midpoint:]) + midpoint
leftx_base = np.argmax(histogram[200:500]) + 200
rightx_base = np.argmax(histogram[800:1100]) + 800
# Choose the number of sliding windows
nwindows = 18
# Set height of windows
window_height = np.int(combined.shape[0]/nwindows)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = combined.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
# Set the width of the windows +/- margin
margin = 100
# Set minimum number of pixels found to recenter window
minpix = 50
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
# Step through the windows one by one
for window in range(nwindows):
# Identify window boundaries in x and y (and right and left)
win_y_low = combined.shape[0] - (window+1)*window_height
win_y_high = combined.shape[0] - window*window_height
win_xleft_low = leftx_current - margin
win_xleft_high = leftx_current + margin
win_xright_low = rightx_current - margin
win_xright_high = rightx_current + margin
# Draw the windows on the visualization image
cv2.rectangle(out_img,(win_xleft_low,win_y_low),(win_xleft_high,win_y_high),(0,255,0), 2)
cv2.rectangle(out_img,(win_xright_low,win_y_low),(win_xright_high,win_y_high),(0,255,0), 2)
# Identify the nonzero pixels in x and y within the window
good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0]
good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0]
# Append these indices to the lists
left_lane_inds.append(good_left_inds)
right_lane_inds.append(good_right_inds)
# If you found > minpix pixels, recenter next window on their mean position
if len(good_left_inds) > minpix:
leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
if len(good_right_inds) > minpix:
rightx_current = np.int(np.mean(nonzerox[good_right_inds]))
# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
In [383]:
# Generate x and y values for plotting
ploty = np.linspace(0, combined.shape[0]-1, combined.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
plt.imshow(out_img)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
Out[383]:
Assuming you already have the points, there is no need estimate sliding window again
In [376]:
# Assume you now have a new warped binary image
# from the next frame of video (also called "binary_warped")
# It's now much easier to find line pixels!
nonzero = combined.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
margin = 100
left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] - margin)) & (nonzerox < (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] + margin)))
right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] - margin)) & (nonzerox < (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] + margin)))
# Again, extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
# Generate x and y values for plotting
ploty = np.linspace(0, combined.shape[0]-1, combined.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
In [377]:
# Create an image to draw on and an image to show the selection window
out_img = np.dstack((combined, combined, combined))*255
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
# Generate a polygon to illustrate the search window area
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))])
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin, ploty])))])
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))])
right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin, ploty])))])
right_line_pts = np.hstack((right_line_window1, right_line_window2))
# Draw the lane onto the warped blank image
cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,255, 0))
cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,255, 0))
result = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
plt.imshow(result)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
plt.xlim(0, 1280)
plt.ylim(720, 0)
Out[377]:
Goal 6: Determine the curvature of the lane and vehicle position with respect to center¶
First calculate the radius of curvature in pixel space
In [217]:
# Define y-value where we want radius of curvature
# I'll choose the maximum y-value, corresponding to the bottom of the image
y_eval = np.max(fity)
left_curverad = ((1 + (2*left_fit[0]*y_eval + left_fit[1])**2)**1.5) / np.absolute(2*left_fit[0])
right_curverad = ((1 + (2*right_fit[0]*y_eval + right_fit[1])**2)**1.5) / np.absolute(2*right_fit[0])
print(left_curverad, right_curverad)
# Example values: 1926.74 1908.48
Then calculate radius of curvature in real world space, based on the lane dimensions given in the instructions (30 meters long and 3.7 meters wide)
In [218]:
# Define conversions in x and y from pixels space to meters
ym_per_pix = 30/720 # meters per pixel in y dimension
xm_per_pix = 3.7/700 # meters per pixel in x dimension
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(fity*ym_per_pix, fit_leftx*xm_per_pix, 2)
right_fit_cr = np.polyfit(fity*ym_per_pix, fit_rightx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
# Now our radius of curvature is in meters
print(left_curverad, 'm', right_curverad, 'm')
# Example values: 632.1 m 626.2 m
Goal 7: Warp the detected lane boundaries back onto the original image.¶
In [220]:
# Create an image to draw the lines on
warp_zero = np.zeros_like(combined).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
# Recast the x and y points into usable format for cv2.fillPoly()
pts_left = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
# Draw the lane onto the warped blank image
cv2.fillPoly(color_warp, np.int_([pts]), (0,255, 0))
# Warp the blank back to original image space using inverse perspective matrix (Minv)
Minv = np.linalg.inv(M)
newwarp = cv2.warpPerspective(color_warp, Minv, (curved_img.shape[1], curved_img.shape[0]))
# Combine the result with the original image
result = cv2.addWeighted(undist_img, 1, newwarp, 0.3, 0)
plt.imshow(result)
Out[220]:
Goal 8: Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.¶
In [ ]:
# I will r